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arXiv · 0910.0524

Some perfect cards shuffles (French title: Quelques m\'elanges parfaits de cartes)

Aimé Lachal
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Abstract

In this paper, we study some cards shuffles which are used by magicians. We focus ourselves on the possibility to hit eventually the initial state after several shuffles. This is a classical problem arising in discrete dynamical systems. The computations are performed through an elementary approach, so the paper is easily accessible. ----- Dans cet article, on \'etudie quelques m\'elanges de cartes bien connus du monde de la magie. On examine en d\'etail l'\'eventualit\'e de reconstituer le jeu de cartes initial apr\`es plusieurs m\'elanges cons\'ecutifs. Il s'agit math\'ematiquement d'un probl\`eme de syst\`emes dynamiques discrets pour lequel on recherche explicitement une p\'eriode. Les calculs \'etant pr\'esent\'es de mani\`ere \'el\'ementaire, l'article se veut accessible \`a un large public.

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Aimé Lachal. 2009-10-03. Some perfect cards shuffles (French title: Quelques m\'elanges parfaits de cartes). https://doi.org/10.1051/quadrature/2010001

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